Comparision of ant colony optimization and genetic algorithm models for identifying the relation between flow discharge and suspended sediment load ( Gorgan River-Iran )

Correct estimation of sediment volume carried by a river is very important for many water resources projects. The prediction of river sediment load also constitutes an important issue in hydraulic and river engineering. Conceptual models based on artificial intelligence models, namely, ant colony optimization (ACO) and genetic algorithm (GA) are now being used more frequently to solve optimization problems. Hence, the main purpose of this study was to apply ACO and GA in order to identify the relation between stream flow discharge and sediment loads for Nodeh station at the Gorgan River in Iran. The training and testing data sets were chosen based on the K-fold method of cross validation to find the optimal classifier. Different input combinations of ACO and GA models (that is, ACO1 and GA1: the suspended sediment estimation based on current discharge; ACO2 and GA2: the estimation of suspended sediment based on current, one day of previous discharges; and ACO3 and GA3: the suspended sediment estimation based on current, one and two-day of previous discharges) were chosen based on similar meteorological requirements to those of the suspended sediment equations included in this study. The estimation of the ACO and GA models was also compared with the empirical model, such as the sediment rating curve (SRC) technique. The models were compared based on statistical criteria, namely; regression coefficient (R 2 ), Nash-Sutclif coefficient (CE) and root mean square error (RMSE). The results indicated that the ACO1 model provided better performance in estimating the suspended sediment loads as compared to the ACO models. Also, the GA2 model was more accurate than the GA1 and GA3 models. The findings in this study showed that the performance of the SRC model was more inferior the ACO and GA techniques when the inputs of the GA, ACO and rating curve models comprised only the current discharge. As seen from the results, the ACO1 model approximated that the corresponding observed suspended sediment values were better than the rating curve and GA2 techniques. However, for the peak flow discharge, the GA2 model could predict the suspended sediment better than the ACO2 and SRC models.


INTRODUCTION
The volume and types of particles eroded and transported by the rivers exhibits great geographical and temporal variability.Predicting the sediment load of a river has long been a goal of engineers, hydrologists, sedimentologists, and many other earth scientists (Leopold et al., 1992).Accurate sediment load prediction is very important in planning, designing, operating and maintenance of water resources structures.Empirical relations, such as sediment rating curves, are often applied to determine the average relationship between discharge and suspended sediment loads.This type of models generally underestimates or overestimates the amount of sediment.Notably, direct measurement of sediment loads is very expensive to implement.Various models have been developed so far to identify the relation between discharge and sediment loads.Most of the models, based on the regression method, have some restrictive assumptions.Therefore, it is still necessary to develop an explicit model for the discharge-sediment relationship.Optimization models based on artificial intelligence models, namely, ant colony optimization (ACO) and genetic algorithm (GA) are now being used more frequently to solve optimization problems.In the early 1990s, ACO (Dorigo, 1992;Gambardella et al., 1999;Maniezzo, 1996) was introduced as a novel natureinspired metaheuristic for the solution of hard combinatorial optimization (CO) problems.ACO belongs to the class of metaheuristics (Blum and Rol, 2003;Glover, 2002;Hoos et al., 2004), which are approximate algorithms used to obtain good enough solutions to hard problems in a reasonable quantity of computation time.Since then, ACO algorithms have been applied to different continuous and combinatorial problems, such as the travelling salesperson problem (TSP), the generalized assignment problem (GAP), the multiple knapsack problem (Leguizamon and Michalewicz, 1999), water distribution network design (Mariano and Morales, 1998), and the constraint satisfaction problem (Schoofs and Naudts, 2000).Abbaspour et al. (2001) used the ACO algorithm for estimating the unsaturated soil hydraulic parameters.Zecchin et al. (2003) compared the performance of original ant system with that of max-min ant system (MMAS), a modified version of the ant system proposed by Stutzle and Hoos (2001), for optimization of water distribution networks.Simpson et al. (2001) discussed the selection of parameters used in the ACO algorithm for pipe network optimization problems.More recently, Maier et al. (2003) compared the performance of the ACO algorithm with that of GA for the optimization of water distribution networks.Afshar (2005) proposed a new transition rule for ACO algorithms using elitist strategies and applied the method to pipe network optimization problems.The method was shown to overcome the premature convergence problem encountered by elitist ACO algorithms while improving the convergence characteristics of the algorithms as compared to alternative methods such as MMAS.
GA have been applied to numerous engineering problems such as management of water systems (Cai et *Corresponding author.E-mail: nrezaii2000@yahoo.com.Tel: 00601-73604770.Pour et al. 3585 al., 2001), design of water distribution networks (Savic and Walters, 1999), optimisation of sewer networks (Parker, 2000), calibration and improvement of urban drainage systems (Liong, 1995;James, 2002).In most applications, single objective GA were used such that only one criterion of optimisation was evaluated at a time and this is mainly due to the inadequate ability of single objective GA to deal with more than one objective.GA has been used frequently in the engineering problems in recent years.Sen and Öztopal (2001) used GA to predict precipitation occurrence.GA are also used in the optimization and operation of groundwater resources design uncertainties in the hydraulic conductivity and they also provide solution of more complex nonlinear problems when compared with traditional gradient based approaches (Espinoza et al., 2005;Hilton et al., 2005;Mahinthakumar et al., 2005).The sediment was predicted from discharge measurements using GA by Altunkaynak (2009).Altunkaynaka and Wang (2010) proposed a new adaptive prediction approach termed Geno-Kalman filtering (GKF), combining GA and Kalman filtering techniques for accurate prediction of suspended sediment concentration (SSC).Their model is formed in three steps.Firstly, discharge and suspended sediment concentration are related by using dynamic linear model.Secondly, an optimum transition matrix relating these two state variables is obtained by Genetic Algorithms (GAs), and an optimum Kalman gain is calculated.Thirdly, Kalman filtering is used to predict the suspended sediment concentration from discharge measurement.They applied the proposed method to measurements at the Mississippi river basin in St. Louis, Missour.
Altunkaynaka (2010) developed some models for predicting suspended soild concentration based on 10 different scenarios for lake Okeechobee in Florida.Extensive data, including wind speed, flow velocity, flow direction and SSC, have been collected.They predicted the SSC by the Kriging interpolation technique.Sen et al. (2004) proposed a new approach for sediment concentration prediction, and provided that there are measurements of discharge and sediment concentration.The basis of their methodology is a dynamic transitional model between successive time instances based on two variables, namely, discharge and sediment concentration measurements.The transition matrix elements are estimated from the measurements through a special form of the artificial neural networks as perceptrons.They achieved the sediment concentration predictions from discharge measurement through a perceptron Kalman filtering (PKF) technique.
The aim of this study is to obtain the relation between suspended sediment discharge and flow discharge for estimation of suspended sediment by using two optimization models that consist of ACO and GA and empirical model (SRC) for Nodeh station at Gorgan-river in Iran.Also, the result of each model was compared together in this study.In this study, the ACO (main aim of Sci.Res.Essays study) was developed because: 1) ACO imposes no continuity requirement on the objective function, and they can solve problems with discrete decision variables; 2) ACO usually does not get trapped to a local-optimal solution, and they can find a near-optimal solution with a high probability; 3) ACO generates several near-optimal solutions, and they can provide sufficient flexibility in decision making; 4) ACO have parallel processing potential, and they can generate faster solution in real (clock) time.

MATERIALS AND METHODS
The optimization and empirical models were used for estimating the suspended sediment in this investigation.The sediment rating curve through bias correction factor was used for the empirical models.The optimization models consisted of the ACO and GA models that were used for estimating the suspended sediment.GA was obtained from MATLAB toolbox, whereas ACO was developed for estimating the suspended sediment in C ++ .For all the models, the daily flow discharge and the suspended sediment discharge measurements were used.

Empirical model or sediment rating curve (SRC)
In spite of very different methods for developing the rating curves, the most common method is the power function of the form where exp is the exponential function and s is the standard error of the regression equation.In the applications, Equation 2 is the sediment rating curve with bias correction factor was used for suspended sediment estimation.

Optimization models
The estimation of the suspended sediment depended only on the current discharge, because of the empirical models such as the sediment rating curve; in this study, flow discharges from the previous one-and two-days were also considered to improve the relationship between suspended sediment discharge and flow discharge, because the suspended sediment discharge has a relationship with discharges from the current, as well as from the previous one-and two-days.
The following equation shows the developed rating curve for the suspended sediment estimation: where s Q is the discharge of suspended sediments ( day ton ); The best unknown coefficients for a, b, c and d for the improved rating curve were obtained by minimizing the root mean square error (RMSE) between the observed suspended sediment discharge and the estimated suspended sediment discharge used (Equation 4).The training data was used to obtain the unknown parameters, and after that, obtained parameters were used for the test period.For minimizing the RMSE between the observed suspended sediment discharge and the estimated suspended sediment discharge using Equation 4, the developed ACO and GA approaches were used.Considering the use of the flow discharge for the improved rating curves by GA and ACO, three sub-models were being created for each of them.If the data of the current day discharge were used for estimating the suspended sediment in Equation 4, the corresponding models of ACO and GA were called ACO1 and GA1; whereas, if the data of the current and one-day previous discharges were used, they were then called ACO2 and GA2.When the current, one and two-day previous discharges were used, the ACO and GA were called ACO3 and GA3.Table 1 summarises the parameters that were used for each model.

GA
This global optimisation (GA) procedure is based on the Darwinian principle of survival of the fittest.Applied to a biological community, it is the principle by which chances of survival of an entire community within a particular environment are increased by discarding inferior members and replacing them by superior offspring.The probability of survival of the community increases as it develops characteristics required to extract maximum benefit from resources within its new environment.This stage is reached over a period spanning many generations and is the result of improving genetic combinations of individual members through reproduction of the fittest.Theoretically, a near optimal solution could perhaps be obtained even within the initial population, if it were possible to formulate a parameter set by taking the best value of each parameter across population members.Given a sufficiently large population, every parameter would assume values evenly distributed over its parameter range.Careful formulation of the genetic plan is required to produce balance between exploitation of the entire search space and exploration of the interesting regions of attraction.
In this part of this research, genetic algorithm improved the sediment rating curve for one and two days before the current discharge.GA with the training data minimized the RMSE between the observed suspended sediment discharge and the simulated suspended sediment discharge for obtaining the coefficient of Equation 4. The best coefficient was found when the lowest RMSE was obtained and the GA stopped.The calculated coefficient through GA was then used for the test period.The following is the first description of the objective function for genetic algorithm.In this study, the objective function was to find a factor set  that minimized the general function by using GA: Where g is the objective function;  is the vector of input factor; l is the number of observed variables;

day ton
). Careful formulation of the genetic plan was required to produce the balance between the exploitation of the entire search space and the exploration of the interesting regions of attraction.For this research, all the functions were examined together for finding the best function.GA may achieve this best combination via its genetic plan, which is a procedure consisting of the following operators: 1) Selection, which randomly chooses a sub-set of individuals for mating from among the whole population; 2) Replacement, which is the mechanism of incorporating into the original population the offspring resulting from mating at the expense of inferior individuals; 3) Crossover, which is the method of swapping genes during mating of selected individuals to produce offspring; 4) Mutation, which randomly alters selected genes in chromosomes and which will be discussed subsequently.
These steps are repeated until a certain error percentage is achieved between two final successive solutions.In the first step of the algorithm, initial population is constituted through the chromosomes that are selected randomly.The number of chromosomes in the population is decided by the user.This population changes by certain rules in order to optimize the target function.Each chromosome should be evaluated by considering their objective function to find the optimum solution.During the evolution of the solution population, some chromosomes depart from the process while stronger ones remain in the updated population.In order to constitute the new generation, chromosomes that provide the most suitable conditions for objective function are selected by using Roulette wheel.This wheel is partitioned into sections of which the widths are determined according to the objective function.So, the chromosomes which have best objective function value have a more chance to be selected as members for the next generation.The new generation is evolved from the current generation by applying some genetic operators such as cross-over and mutation.These operations are repeated until the objective function is achieved.The number of iterations required to obtain the optimal coefficient values depend on the initial population.If the initial population is close to solution point, the algorithm would reach the solution with less iteration.Since GA produce many solution points, they put forward the relationship between discharge and sediment by forming more than one curve using a and b parameters in Equation 4. The flow chart of the genetic algorithm used in this study is as shown in Figure 1.

ACO
ACO is now being used more frequently to solve optimization problems other than those for which they were originally developed.However, the application of ACO to water resources problems is rather recent.In this part of the research, ACO can improve the sediment rating curve for one and two-day discharges before the current discharge.ACO with the training data (from sample data) minimized the RMSE between the observed suspended sediment discharge and the simulated suspended sediment discharge in order to obtain the coefficient of Equation 4. ACO continues until the lowest RMSE is obtained.The best coefficient was found when the lowest RMSE was obtained, after which ACO was stopped.The calculated coefficient was used for the test period (from sample data).
Application of ACO to estimated suspended sediment: During the past several decades, considerable advances have been made in the mathematical description of water flow and suspended sediment transport.A large number of models are now available for predicting the subsurface flow and suspended sediment.Still, effective application of such models to practical field problems suffers from the lack of knowledge of model parameters and their uncertainties.In order to deal with the issue of model factor identification, inverse modelling (IM) from ant system (AS) algorithm provides that constituted estimation of input factors from readily measurable model output variables.Input factors are obtained by minimizing an objective function describing the difference between the measured and simulated data (Abbaspour et al., 2001).
The first in this part of the study was to describe the objective function.In this study, the objective function was the same with the objective earlier explained in the part of GA.As mentioned previously, the objective function is to find a factor set  that minimizes the general function repeated here for convenience: In the ACO algorithm, a colony of artificial ants contributes in finding good solutions to discrete optimization problems.Application of the ACO algorithm to arbitrary combinatorial optimization problem requires that the problem can be projected on a graph (Dorigo, 1996).Consider a graph G = (J, γ, U), in which J = { The main concept behind the algorithm can be summarized in the following steps: 1) Depict each unknown factor by an interval based on the available information for the imaginary factor  , as shown in Figure 2; 2) Discrete each interval into a number of level, and let the middle of each layer represent that layer; 3) Run the simulation model of the selected subset of all the possible factor combinations (a loop); 4) Grade each layer on the basis of the smallness of the value of the objective function received higher grade; 5) Remove from the ends of the factor intervals the level with small or no grade, thereby, decreasing the initial range of factor uncertainty, and finally; 6) Repeat the process until a desired stopping rule is reached.
In the algorithm, each layer, which is initially set to a grade of zero, receives a grade of 1 if the numerical quantity of the objective function g, for that layer satisfies the condition ( , where cr g is the user defined numerical quantity (Abbaspour et al., 2001).

Explication of the ACO:
The ACO problem can be described as follows: let , as given by Equation 6 be a continuous and bounded function, and  be a b-dimensional state vector.The objective is to find the state vector  that minimizes g (  ).Without the loss of generality, D can be taken as the hyper parallelepiped:

Attribute tasks to ant agentive role:
The total number of ant m in the colony is chosen because any ant must follow one nerve tract.Acting like an agentive role, each ant has the following tasks: 1) Selecting a nerve tract from the nerve tract list and remembering the numerical quantities of the factor level along its nerve tract; 2) Passing the factor numerical quantities to a simulation programme at the end of the nerve tract; 3) Calculating the numerical quantity of the objective function for its nerve tract, and 4) Placing a certain pheromone in the case of real ants on the basis of the numerical quantity of the objective function.
Once all ants complete the aforementioned circuit, one ant cycle or one loop is completed (Abbaspour et al., 2001).
Counting the trail and grading factor level: Pheromone trails play an important function in the foraging behaviour of the real ant colonies.While walking from food sources to the nest and vice versa, ants stick on the ground a substance called pheromone, forming in this way a pheromone trail.Ants can smell pheromone and, when choosing their way, they tend to choose, in probability, routes marked by strong pheromone densities (Abbaspour et al., 2001).
The pheromone trail acts as a form of indirect social relation called stigmergy helping the ants to find their way back to the food source or the nest.In ACO, pheromone trails are the only social relation channel among the ants and play a major role in the utilization of collective knowledge of the colony (Abbaspour et al., 2001).

Let
) 1 ( u  be the intensity of pheromone on nerve tract u (u = 1,…N) and cycle 1.Ants must place the same quantity of pheromone on the layers that they follow.In the Travelling Salesman Problem (TSP), the trail intensity is defined as a function of the length of a route.In this problem, we used the numerical quantity of the objective function of a nerve tract to ascribe the trail.where u g is the numerical quantity of the objective function for the u th nerve tract, cr g (will be defined later) is a critical numerical quantity and min g is the minimum numerical quantity of the objective function for a cycle (Abbaspour et al., 2001).
The aforementioned Equation ( 7) posits that the nerve tracts with numerical quantities of the objective function larger than cr g receive no pheromone, while below cr g , the intensity of trail is exponentially larger for smaller numerical quantities of the objective is a set equals to an arbitrary numerical quantity of 100 (this numerical quantity would be equivalent to Q in the TSP, which also incidentally equals 100) (Abbaspour et al., 2001).
In order to determine how to update the factor, we defined the term grade i S for each layer counted by the following expression similar to the transition probability of the TSP problem.
where the numerical quantity of A = 1, and count N and T by using, where ij ij   , are respectively the standard deviation and mean of trail of the ij  level (Abbaspour et al., 2001).
where crossing nerve tracts are all the nerve tracts that cross layer ij  (Abbaspour et al., 2001).The work Abbaspour (2001) has more information about this algorithm.

Updating factors and stopping rules:
The counted trail for each nerve tract is used to grade a nerve tract.The low grading nerve tracts will vanish and new nerve tracts will evolve around high grading routes (Abbaspour et al., 2001).
Once the grading is completed, the factors are updated by decimating the level with small grades from both ends of the intervals.This results in factors with narrower ranges.Note that, if the high grading level falls on either end of the factor intervals, the factors could be extended in that direction.The system is subsequently reinitialized, with the updated factors and the process repeated.This loop continues until a stopping rule is satisfied.This may occur when: (1) a desired numerical quantity of the objective function is reached, and (2) no changes in the numerical quantity of the objective function are obtained in the consecutive loops.Figure 3 shows the flow chart for ACO.

Study area and data
The Gorgan River watershed is located in the southeast of the Caspian Sea between 54°,02' -56°,16' east longitude and 36°,34' -37°,47' north latitude.The Gorgan River originates from the high lands of the Alborz mountain chains at the eastern part of the watershed.After passing through the city of Gonbad Kavous, it enters into Voshmgir Dam and finally joins the Caspian Sea.The watershed of Gorgan River spreads over an area of 13170 km 2 approximately, 7838 km 2 (60%) of which accounts for the watershed highlands, and the remainder includes foothills and plains.Nearly 8500 km 2 of the watershed is covered by the Basin of Gorgan River, which extends to the Voshmgir Dam. Figure 4 shows the location of Gorgan River basin and Voshmgir Dam.
In this study, the mean river flow discharge and the suspended sediment concentration data at Nodeh station on the Gorgan River in Iran were used.These data, gathered from the Water Resource in Golestan province from 1978 until 2008, were divided into two partitions, that is, one for training and the other for testing.It was important to separate the data sets into two separate sets, that is, one to be used for training and the other for testing the results obtained from the training.K-fold cross validation was used in the field of machine learning to determine how accurately a learning algorithm would be able to predict data that it was not trained on.

Efficiency criteria
Here, the efficiency criteria used in this study are presented and evaluated.These are the three criteria: coefficient of determination, Nash-Sutcliffe efficiency, and RSME present in the model simulation.

Coefficient of determination (R 2 )
The coefficient of determination R 2 is defined as the squared value of the coefficient of correlation according to Bravais-Pearson.It is calculated as: With O observed and P predicted values.R 2 can also be expressed as the squared ratio between the covariance and the multiplied standard deviations of the observed and predicted values.Therefore, it estimates the combined dispersion against the single dispersion of the observed and predicted series.The range of R 2 lies between 0 and 1 which describes how much of the observed dispersion is explained by the prediction.A value of zero means no correlation at all, whereas a value of 1 means that the dispersion of the prediction is equal to that of the observation.The fact that only the dispersion is quantified is one of the major drawbacks of R 2 if it is considered alone.A model which systematically over-or under predicts all the time will still result in good R 2 values close to 1.0 even if all predictions were wrong.

Nash-Sutcliffe efficiency
The coefficient of efficiency (CE) proposed by Nash and Sutcliffe (1970) is defined as one minus the sum of the absolute squared where CE is the coefficient of efficiency, N is the number of data points, O is observed value and P is predicted value.Nash-Sutcliffe efficiencies can range from −∞ to 1.An efficiency of 1 (CE = 1) corresponds to a perfect match of model discharge to the observed data.An efficiency of 0 (CE = 0) indicates that the model predictions are as accurate as the mean of the observed data, whereas an efficiency less than zero (CE < 0) occurs when the observed mean is a better predictor than the model or, in other words, when the residual variance, is larger than the data variance.

RMSE
where, RMSE is the root mean square error, N is the number of data points, O is observed value and P is predicted value.

RESULTS
The scatter plots of the Nodeh station data for determining the relationship between the discharge and sediment data were used, as shown in Figure 5.It can be seen that there was a non-linear and scattered relationship between the discharge and sediment data for this station.The daily statistical parameters of the stream flow and sediment data were  2.
The results of each model are shown in the subsequently.Considering the presentation of results from the each month, it took more time and attention than only the results of April declared.

Sediment rating curve
As for the SRC model, the daily discharge and sedimentation data of 30 years were used for the monthly method.Prior to application, the SRC data were divided into two parts, namely, calibration and validation.The training data was used to find the model parameters  (coefficients of a and b), while the rest of the data was employed for validation of the model.On the other hand, in Figure 6, the scatter plot for the observed and estimated suspended sediments for April was drawn by the SRC model.Meanwhile, Figure 7 shows the scatter plot of the discharge against the observed suspended sediment load and the estimated suspended sediments by SRC, whereas Table 3 displays the RMSE, coefficient of determination (R 2 ) and Nash's Efficiency (CE) values.

GA
Several input combinations are checked using GA to estimate suspended sediment load for the Nodeh station.The RMSE, coefficient of determination (R 2 ), Nash-Sutcliffe  efficiency (CE) and coefficients that provide the best relationship between discharge and the sediment load of GA models in test period are shown in Table 4.For GA optimization, constant parameters, sets of a, b, c and d parameters were obtained from training data.The scatter plot of the discharge against the observed suspended sediment load and the estimated suspended sediment by GA models of April is as shown in Figure 8. Also in Figure 9, the scatter plot for the observed and estimated suspended sediment for April is drawn by parameters found as a result of GA optimization.

ACO
For the Nodeh station, the RMSE, coefficient of determination (R 2 ), Nash-Sutcliffe efficiency (CE) and coefficients that provide the best relationship between discharge and the sediment load of ACO models in test period are given in Table 5.For ACO optimization, parameters, sets of a, b, c and d were obtained from

Conclusions
Alternatively, in this study, the parameters obtained by ACO and GA produced many sets of coefficient providing a relationship between w Q and s Q .The study showed the ability of the ACO technique to model the relationship between the stream flow and the suspended sediment.
The model provides a practical way for sediment estimation, producing accurate results and encouraging the use of ACO in other aspects of water engineering studies.The suspended sediment estimations based on the ACO models were compared with GA and sediment rating curves.For the monthly suspended sediment estimation, the results indicated that the ACO1 model provided better performance in estimating the suspended sediment loads as compared to other ACO models.Also, the GA2 model was more accurate than GA1 and GA2.It can be obviously seen from the results that the ACO1 model performed much better than the rating curve techniques.However, the GA2 technique had slightly better value of RMSE than the SRC model.The accuracy of the SRC models seemed to be better than the ACO3 model from the variety of ACO models.In addition, it can be observed from the results that the performance of the SRC model was more inferior than ACO and GA techniques when the input to both GA and ACO and the rating curve model was only the current discharge.Also, after using the ACO model, the GA model was better than SRC.As seen from the results, the ACO1 model approximated the corresponding of the observed suspended sediment values better than the rating curve and GA2 techniques.The ACO1 seemed to have a better accuracy than the GA2 model.It was seen from the results that both the low and high sediment values and in general the overall shape of the sediment time series were closely approximated by the ACO1 for the monthly method.However, for the peak flow discharge, the GA2 could predict the suspended sediment better than ACO1 and SRC.From the mentioned results, it can be concluded that the suspended sediment discharge had high relationship with the current discharge and one-day previous discharge, whereas, it was an infirm relation between the two-day previous discharge and the suspended sediment discharge.There were a lot of research studies in the literature that looked at the prediction of sediment loads.However, only Altunkaynak (2009) applied the GA for suspended sediment estimation for the lower Mississippi river basin.He proposed a relationship between the sediment loads and the discharge by using GA.His results showed that GA provided better solutions than regression model (RM) with respect to the errors calculated by R 2 and mean relating error (MRE).Considering Altunkaynak (2009) research for the sediment loads, the results of this investigation were also confirmed.However, ant colony optimization is applied more in water resource engineering, such as ground water, pipe network optimization and water distribution network.Nevertheless, there is no application for surface water resource, especially in suspended sediment estimation.In addition, Abbaspour et al. (2001) used the ACO algorithm for estimating the un-saturated soil hydraulic parameters.The results obtained with the ant colony parameter optimization method were very promising, that is, in eight different applications, they were able to estimate the true parameter within a few percent.Some of the advantages and disadvantages of the ACO algorithm and GA can be summarized as follows: Pour et al. 3603 1) Optimization can be made through continuous or noncontinuous variables.
2) It is possible to start searching from many different points at solution space so that through numerous variables, global optimization is possible.
3) Even in case of target functions with extreme values, optimization is possible.4) ACO and GA produce a set of solution points during an adaptive and dynamic system structure evolution.5) GA and ACO approaches provide the most suitable solution in the quickest way for an optimization problem.
The GA and ACO solution has different facets than classic optimization methods.They seem as indefinite methods due to the random sampling procedure and rules at their basis.6) One of the advantages of GA and ACO is its ability to generate more than one optimum solution points.On the other hand, SRC with the limiting assumptions can only estimate one solution point.
Another reason why the ACO and GA approach should be preferred is the independency of them from restrictive assumptions.
The power of GA comes from the fact that the technique is robust and can deal successfully with wide range of difficult problems.GA is not guaranteed to find the global optimum solution to a problem, but they are generally good at finding acceptably good solutions to problems acceptably quickly.Where specialized techniques exist for solving particular problems, they are likely to outperform GA in both speed and accuracy of the final result.
Disadvantages of these classical models, same ACO are that the calculations take too much time.In ACO degree of parameter, conditioning may be directly controlled through iteration.The more iteration we perform, the conditioned parameters being sought will become on the set, measured data.In general, we do not recommend obtaining highly conditioned parameters, as they will perform poorly when simulating other variables not included in the objective function.To find a global maximum, two techniques must be used for any efficient optimization algorithm: exploration to investigate new and unknown areas in the search space, and exploitation to make use of knowledge found at points previously visited to help find better points.These two requirements are contradictory, and a good search algorithm must find a trade off between the two.

Q
is the stream discharge in ( s m 3 ); a, b are the coefficients that provide the best relationship between discharge and the sediment load.These parameters are generally obtained by least squares method.For a given set of s Q and w Q data, only one solution point (a and b) values are obtained.In this case, a and b coefficients are accepted as constant through all process.After logtransformation to the arithmetic domain and application of the Ferguson (1986) correction factor, the sediment load occurring at a specific discharge can be estimated using the following expression: b

s m 3
); a, b, c, and d are the determination coefficients.

oQ
is the measured value of suspended sediment discharge of the ith variable (
of decision points at which some decisions are to be made; γ = { il  } is the set of options; L = 1,2,...,l, at each of the determination points; i = 1,2,...,n; and finally U = { il u } is the set of costs associated with options γ = { il  }.

.
If each layer is represented by the numerical quantity at the middle of the layer, then there will be W = nerve tracts through the space of the input factors.The aforementioned decretive scheme for the three factors is schematically shown in Figure2.While having more levels would speed up the convergence of the ACO problem, this advantage should be balanced against the speed of the simulation programme, which rapidly increases as the number of calls to a simulation programme rapidly increases as the number of level increases.To limit the number of function calls, one could select only a random subset of M or N and invoke parallel processing.Based on Abbaspour experience so far, about 0.8 and 0.5, respectively.The factor A, N and T in Equation 8 control the relative importance of the trail intensity versus sensitivity.Note that any single layer ij  may be the crossroad of many ant nerve tracts.The trail share of each layer ij  form each nerve tract, and can be summed to yield ij  as:

Figure 4 .
Figure 4. Location of the Gorgan River Basin and Nodeh station.
, maximum and minimum of data, respectively.The daily statistical parameters of the stream flow and sediment data are given in Table

Figure 5 .
Figure 5. Suspended sediment load-discharge scatter diagram for all data for the Nodeh station.

Figure 6 .Figure 7 .Figure 8 .
Figure 6.Scatter plot for observed and predicted suspended sediment for test period for various SRC for April.
than the SRC model.Apparently, the ACO1 seemed to have better accuracy than the GA2 model.Moreover, it can be seen from this figure that the ACO1 model estimation was closer to the observed suspended sediment values than the rating curve and GA2 techniques for peak value (especially the SRC).

Figure 12 .
Figure 12.The scatter plot of the discharge against the observed suspended sediment load and the estimated suspended sediment by the best ACO, best GA and SRC models of Nodeh station during test period in April.

Table 1 .
Discharge identity parameter used for corresponding model.

Table 2 .
The daily statistical parameters for monthly flow discharge (m 3 /s) and suspended sediment (ton/day).

Table 3 .
The RMSE (ton/day), coefficient of correlation and determination coefficient of SRC models for test period.